Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22590596 | C2 | semidirect |
| 2. #22590595 | C2 | semidirect |
| 3. #22590589 | C2 | semidirect |
| 4. #22587954 | C2 | semidirect |
| 5. #22587945 | C2 | semidirect |
| 6. #22586256 | C2 | semidirect |
| 7. C71×#2246 | C2 | semidirect |
| 53. C71⋊C16 | D8 | semidirect |
| 65. C16×C71 | D8 | semidirect |
| 106. #2246 | D71 | semidirect |
| 110. C71 | #12519 | semidirect |
| 168. C16 | #11765850 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590596 | 2 |
| #22590595 | 2 |
| #22590589 | 2 |
| #22587954 | 2 |
| #22587945 | 2 |
| #22586256 | 2 |
| C71×#2246 | 2 |
| #12519 | 71 |